Sampling (Continued)

Spacing in the Crossrange Direction

Spacing in the crossrange direction was also examined (figure 19). The 20- by 5-foot spacing was compared to a 20- by 10-foot spacing.

Illustrations of the center section of the test area showing the 20- by 5-foot spacing and the 20- by 10-foot spacing.

Figure 19—The original 5-foot spacing was increased
to 10 feet in the crossrange direction to evaluate
sampling density.

Figure 20 shows quantile-quantile (QQ) plots. These plots are used to compare the distribution of estimated to observed values. The distributions are equal when x = y or when the data fall on the 45-degree line. In both plots the distributions are similar. The 40-foot QQ plot shows that the wider spacing is not going to pick up unusually high cup weights. In effect, widening the spacing smooths the results. Going from a 20-foot spacing to a 40-foot spacing is probably too great a jump.

Two quantile-quantile plots comparing the observed and predicted values (gpc) for the changes indicated in figures 18 and 19.

Figure 20—Quantile-quantile (QQ) plots comparing distributions.

However, a 25-foot spacing may be appropriate. More information on the comparison of spacing in the direction of flight can be found in the appendix.

The 10- versus 5-foot comparison shows almost identical distributions. The correlation is high (0.97, table 7) meaning the change in spacing is not producing a big change in the results. Considering the time and costs, the 5-foot spacing would probably not be necessary.

Table 7—Comparison of observed gpc (gallons per 100 square feet) values from the center section of cups with 5-foot spacing with predicted gpc values from the center section of cups with 10-foot spacing. MAE is mean absolute error and MSE is mean squared error.


Drop 201	TRUE	Triangulation (gpc)
Mean	0.74	0.72
Standard deviation	0.85	0.79
Minimum	0.00	0.00
1st quartile	0.01	0.03
Median	0.33	0.39
3rd quartile	1.50	1.37
Maximum	3.09	2.64
Correlation		0.97
n	48	48

Summary statistics for error distribution
Drop 201	Triangulation (gpc)
Mean	-0.02375
Standard deviation	0.204
Minimum	-0.965
1st quartile	-0.043
Median	0.003
3rd quartile	0.048
Maximum	0.430
MAE	0.110
MSE	0.041
n	48

Staggered Spacing

If drop-test data are viewed as spatial data, it is assumed that two cups close together are more likely to have similar values than two that are far apart (Isaaks and Srivastava 1989). To reduce the distance between cups, the stakes can be staggered. Without staggering, the greatest distance between two stakes is 22.36 feet. This distance can be reduced to 20.62 feet with staggering. Even though the difference in distance is less than 10 percent, this small step can help improve accuracy.

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